Analysis of Adjacency, Laplacian and Distance Matrices of Zero Divisor Graphs of 4-Radical Zero Completely Primary Finite Rings

https://doi.org/10.51867/scimundi.mathematics.4.2.7

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Palavras-chave:

Completely Primary Finite Rings, Matrices of Zero Divisor Graphs

Resumo

This study is an extension of our study on matrices of zero divisor graphs of classes of 3-radical zero completely primary finite rings. It focusses on Matrices of a class of finite rings R whose subset of the zero divisors Z(R) satisfies the condition (Z(R))4 = (0) and (Z(R))3 = (0) for all characteristics of R that is; p, p2, p3 and p4. We have formulated the zero divisor graphs Γ(R) of R and associated them with three classes of matrices, namely, the Adjacency matrix [A], the Laplacian matrix [L] and the Distance matrix [dij]. The study has further characterized the properties of the graphs Γ(R) and the matrices mentioned.This study is an extension of our study on matrices of zero divisor graphs of classes of 3-radical zero completely primary finite rings. It focusses on Matrices of a class of finite rings R whose subset of the zero divisors Z(R) satisfies the condition (Z(R))4 = (0) and (Z(R))3 = (0) for all characteristics of R that is; p, p2, p3 and p4. We have formulated the zero divisor graphs Γ(R) of R and associated them with three classes of matrices, namely, the Adjacency matrix [A], the Laplacian matrix [L] and the Distance matrix [dij]. The study has further characterized the properties of the graphs Γ(R) and the matrices mentioned.

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Publicado

2024-08-06

Como Citar

Ndago, F. O., Oduor, M. O., & Ojiema, M. O. (2024). Analysis of Adjacency, Laplacian and Distance Matrices of Zero Divisor Graphs of 4-Radical Zero Completely Primary Finite Rings. SCIENCE MUNDI, 4(2), 61–80. https://doi.org/10.51867/scimundi.mathematics.4.2.7

Edição

Vol. 4 N.º 2 (2024): Jul-Dec 2024

Secção

Articles
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Direitos de Autor (c) 2024 Frank Omondi Ndago, Maurice Owino Oduor, Michael Onyango Ojiema

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Este trabalho encontra-se publicado com a Creative Commons Atribuição-NãoComercial 4.0.

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